I have two unknowns here, I thought there might be a way of finding either acceleration or thrust using mass, propellant mass and propellant consumption?
I have searched through my HSC texts and haven't been able to find an equation where I can find 'a' or 'T' without needing one to find the other.

I see what you mean, so I could answer this question quite simply with; T>3.4*10^6?

However I have just read part (b) of the question which says 'If that thrust is sustained, find the time over which the first stage operates and acceleration of the vehicle at that time.'

So, I can find how long the first stage will operate using this method;
Mass of propellant/Consumption rate of propellant
= 2.0*10^6/1.4*10^4
= 142.85 seconds = 2 minutes 23 seconds (approx.)

Acceleration of the vehicle at that time? As we are assuming thrust>weight perhaps I could use a number slightly greater than the weight but still close, 3.41*10^6?
As you can see I am still stuck with two unknowns :(

Methinks there is a lift-off acceleration specified in the textbook, which you have failed to disclose.

Nope, no lift-off acceleration (otherwise this question would be simple), and it would be strange for them to expect me to use a random number greater than the weight because if I were to do that, I would have to use an infinitely close number?! Especially considering this is an assignment and that would be very ambiguous..

There is something missing. One cannot compute the acceleration or thrust of a rocket knowing only the fuel consumption rate, fuel weight, and mass of the rocket.

Think of it this way: You are sitting on a flatbed railroad car with a pile of uniformly-sized rocks, with the car in turn sitting on a frictionless track. The car will accelerate when you throw rocks at some rate from the car. The acceleration increases if you instead use some device that ejects rocks at a very high speed, even if you keep the number of rocks ejected per minute the same as the rate at which you threw them.

I fully understand the concepts involved. I am merely trying to think of alternative ways to solve this problem.

I will find help with this elsewhere. You D H, as a 'mentor', are very condescending. A mentor is supposed to stimulate thought and be suggestive. I don't find this "Please provide the relevant information. You have left out something very important because you think it is irrelevant. That missing information is very relevant." at all thought-stimulating, suggestive, supportive, helpful, intuitive, enlightening or open-minded. I find it condescending and arrogant. I cannot fathom how a person of your calibre (engineering degree) is unable to suggest any form of alternative to put this problem remotely close to a solution.

I DO however thank NascentOxygen for sharing your suggestions and even still when you could not find a solution, suggesting an alternative to find more information.

Staff: Mentor

I'm certain that when you ask your teacher how this question is to be answered, s/he will realize there's a missing detail. Please come back and let us know what it is. You can't be expected to solve a problem where an essential piece of information has been left out, albeit inadvertently.

In the event of this being an exam question, you may still be eligible for full marks if you were to identify those details which are needed to be able to fully answer the question.

I love this. Nasty of you to bite the helping hand. As you notice, DH is magnanimous enough to understand your outcry is just an utterance of frustration.

With only one google apollo launch thrust you find back your T > 3.33 x 107 N and the one or two bits extra info the missing of which caused all this fuzz :

•Stage I was called the S-IC. It had five rocket engines that used liquid oxygen and kerosene as fuel. Each engine produced 1.5 million pounds (6,675,000 newtons) of thrust. Together, the engines could generate 7.5 million pounds (33,375,000 newtons) of thrust. Think of thrust as the strength of a rocket engine. This thrust pushed the entire vehicle assembly more than 36 miles (57.9 km) vertically at a speed of 9,030 feet (2,752 m) per second (fps). At that point, the S-IC's engines shut off. Explosive bolts connecting S-IC to the rest of the Saturn V vehicle detonated, jettisoning stage I into the Atlantic Ocean.​

Even if it was your teacher that accidentally left one of these bits, you owe DH an apology. You're smart enough to understand that getting angry is one thing, making up another. And that running away is not a solution.

Oh, and the launch vehicle is a Saturn missile. Apollo is the spacecraft. Now that is definitely something to pass on to teacher...

But perhaps teacher isn't doing so badly: At launch time the acceleration of the missile isn't all that big (it's a stately thing to see such a launch) and the speed isn't either. In fact we don't even need T > m0g: T=m0g will make the thing take off just as well thanks to dm/dt<0. Let's stick to the = sign.

Staff: Mentor

But perhaps teacher isn't doing so badly: At launch time the acceleration of the missile isn't all that big (it's a stately thing to see such a launch) and the speed isn't either. In fact we don't even need T > m0g: T=m0g will make the thing take off just as well thanks to dm/dt<0. Let's stick to the = sign.